Applying the proto-theory of design to explain and modify the parameter analysis method of conceptual design

This article reports on the outcomes of applying the notions provided by the reconstructed proto-theory of design, based on Aristotle’s remarks, to the parameter analysis (PA) method of conceptual design. Two research questions are addressed: (1) What further clarification and explanation to the approach of PA is provided by the proto-theory? (2) Which conclusions can be drawn from the study of an empirically derived design approach through the proto-theory regarding usefulness, validity and range of that theory? An overview of PA and an application example illustrate its present model and unique characteristics. Then, seven features of the proto-theory are explained and demonstrated through geometrical problem solving and analogies are drawn between these features and the corresponding ideas in modern design thinking. Historical and current uses of the terms analysis and synthesis in design are also outlined and contrasted, showing that caution should be exercised when applying them. Consequences regarding the design moves, process and strategy of PA allow proposing modifications to its model, while demonstrating how the ancient method of analysis can contribute to better understanding of contemporary design-theoretic issues

Stochastic Line-Motion and Stochastic Conservation Laws for Non-Ideal Hydromagnetic Models. I. Incompressible Fluids and Isotropic Transport Coefficients

We prove that smooth solutions of non-ideal (viscous and resistive) incompressible magnetohydrodynamic equations satisfy a stochastic law of flux conservation. This property involves an ensemble of surfaces obtained from a given, fixed surface by advecting it backward in time under the plasma velocity perturbed with a random white-noise. It is shown that the magnetic flux through the fixed surface is equal to the average of the magnetic fluxes through the ensemble of surfaces at earlier times. This result is an analogue of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein-Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the non-ideal MHD equations, but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall magnetohydrodynamics and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux-conservation remains stochastic in that limit.Comment: 20 pages, no figures, submitted to J. Math. Phys

A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

La réaction d’hémagglutination (Réaction de Middlebrook-Dubos ) dans la paratuberculose bovine (Entérite chronique hypertrophiante, maladie de Johne)

Gernez-Rieux Charles, Tacquet Albert, Gaumont R., Verge Jean, Cauchy Laurent. La réaction d'hémagglutination (Réaction de Middlebrook-Dubos) dans la paratuberculose bovine (Entérite chronique hypertrophiante, maladie de Johne). In: Bulletin de l'Académie Vétérinaire de France tome 103 n°9, 1950. pp. 465-468

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Computer-assisted liver graft steatosis assessment via learning-based texture analysis

Purpose: Fast and accurate graft hepatic steatosis (HS) assessment is of primary importance for lowering liver dysfunction risks after transplantation. Histopathological analysis of biopsied liver is the gold standard for assessing HS, despite being invasive and time consuming. Due to the short time availability between liver procurement and transplantation, surgeons perform HS assessment through clinical evaluation (medical history, blood tests) and liver texture visual analysis. Despite visual analysis being recognized as challenging in the clinical literature, few efforts have been invested to develop computer-assisted solutions for HS assessment. The objective of this paper is to investigate the automatic analysis of liver texture with machine learning algorithms to automate the HS assessment process and offer support for the surgeon decision process. Methods: Forty RGB images of forty different donors were analyzed. The images were captured with an RGB smartphone camera in the operating room (OR). Twenty images refer to livers that were accepted and 20 to discarded livers. Fifteen randomly selected liver patches were extracted from each image. Patch size was 100 × 100. This way, a balanced dataset of 600 patches was obtained. Intensity-based features (INT), histogram of local binary pattern (HLBPriu2), and gray-level co-occurrence matrix (FGLCM) were investigated. Blood-sample features (Blo) were included in the analysis, too. Supervised and semisupervised learning approaches were investigated for feature classification. The leave-one-patient-out cross-validation was performed to estimate the classification performance. Results: With the best-performing feature set (HLBPriu2+INT+Blo) and semisupervised learning, the achieved classification sensitivity, specificity, and accuracy were 95, 81, and 88%, respectively. Conclusions: This research represents the first attempt to use machine learning and automatic texture analysis of RGB images from ubiquitous smartphone cameras for the task of graft HS assessment. The results suggest that is a promising strategy to develop a fully automatic solution to assist surgeons in HS assessment inside the OR